{"title":"复射影流形的总曲率和贝蒂数","authors":"J. Hoisington","doi":"10.2140/gt.2022.26.1","DOIUrl":null,"url":null,"abstract":"We prove an inequality between the sum of the Betti numbers of a complex projective manifold and its total curvature, and we characterize the complex projective manifolds whose total curvature is minimal. These results extend the classical theorems of Chern and Lashof to complex projective space.","PeriodicalId":254292,"journal":{"name":"Geometry & Topology","volume":"153 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the total curvature and Betti numbers of complex projective manifolds\",\"authors\":\"J. Hoisington\",\"doi\":\"10.2140/gt.2022.26.1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove an inequality between the sum of the Betti numbers of a complex projective manifold and its total curvature, and we characterize the complex projective manifolds whose total curvature is minimal. These results extend the classical theorems of Chern and Lashof to complex projective space.\",\"PeriodicalId\":254292,\"journal\":{\"name\":\"Geometry & Topology\",\"volume\":\"153 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-07-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Geometry & Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/gt.2022.26.1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geometry & Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/gt.2022.26.1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the total curvature and Betti numbers of complex projective manifolds
We prove an inequality between the sum of the Betti numbers of a complex projective manifold and its total curvature, and we characterize the complex projective manifolds whose total curvature is minimal. These results extend the classical theorems of Chern and Lashof to complex projective space.
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